In “What did Warren Spahn know?” I showed different charts for right-handed and left-handed batters; a few readers rightfully suggested that the pitcher handedness should have also been taken into account.

So to see how batters fare when pitcher handedness is controlled for, I will show a chart graphing horizontal location vs. run value charts, with the blue line representing batter performance against same handed pitchers and the maroon line representing batter performance against opposite handed pitchers. I flipped (i.e. multiplied by minus one) the horizontal location for lefthanded batters so that LHB vs. RHP duels are analyzed together with RHB vs. LHP duels and LHB vs. LHP duels with RHB vs RHP ones.

As we have already noted a few weeks ago, each pitch has his peculiar line of effectiveness across the horizonal axis.

So, where do we cut the slices? Sure we would like them to capture the valleys in the charts (different for different pitch types).
If we take five inches as the width of the happy zones for the pitchers here it is where we could center the second and fourth slices.

To get the values in the above table I calculated five inches moving averages for the run value and chose the zones with the lowest value on each side of the plate.

After all this work I still believe that, unless we’d like to have different cut points for each pitch type, we can go with Warren Spahn’s wisdom and take the five inches around each border of the plate.

Does anybody see a better way to cut the slices? Please don’t hesitate to let me know what my eyes have missed!

Some other readers of my first post wished to see something similar for the vertical location, so here we go.
First chart: all the pitches.

Before you ask, I won’t present split results for batter/pitcher handedness: that’s because when I drew the split charts in the preliminary phases of this analysis I didn’t notice any platoon effect.

Here something might seem to go against the conventional wisdom of keeping the ball at knee height, but we have to remember that fastballs account for more than 60 percent of the pitches … and fastball can be effective when delivered up in the zone.

When looking at run value vs. vertical location of the four main pitches we see expected things.

The fastball achieves the best results up in the zone, the change-up low in the zone, the curve low and even out of the zone, the slider doesn’t have a “vertical effect” (apart from the difference between strikes and balls—well, you’ll have less trouble if you keep it down anyway).

I also drew an additional chart for fastballs splitting the fastballs into three (extremely subjective) groups, according to the speed at which they were released. Again no surprises: higher velocity equals higher location of maximum effectiveness.

It’s time to cut the layers.
Looking at the turning points on each graph can lend us some help.

In the table above you see the heights where each pitch type has the minimum run value.
(Note: those heights are relative to a hypothetical batter whose strike zone goes from 19 inches up to 41.5 inches).

Based on these results, the lower third of the strike zone (maybe a little farther down) is the best layer for change-ups; above that, the middle layer would be the one for the fastballs in the low 90s; the upper third of the strike zone (plus some more upstairs) is for the high cheese: fastballs over 95 mph.

Let’s add a layer that goes from the ground to the lower limit of the strike zone and another one from the higher limit to the sky, and we’re done. Curveballs and sliders can be successful in those layers; basically you just have to stay away from the heater’s layer … otherwise you have just thrown a hanger.

Analyzing the pitch location one coordinate at a time may be an oversimplified approach, nonetheless it can give important insights on pitch behavior, as the numerous slices/layers articles by Harry have shown so far. Many other analysts have already produced either heatmaps or lattices showing the combined effect of both horizontal and vertical location on pitching success.

As we have seen in the last graph presented in this article, a few miles of speed change the desirability of pitching to a particular location in the strike zone; this means we need to add another dimension to our plots; then, as Dave Allen has started showing at Baseball Analysts, vertical and horizontal movement can not be left out of the equation.

It seems we’ll have to perform a few tricks in order to plot all these quantities together!